self doubt PnC

Question

In how many ways $10$ different books can be distributed among there student $A, B$ and $C$ such that
$A$ must be given at least $1$ book?

Comments

3^10-2^10? is it correct?Lakshman Patel RJIT

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$3^{10}-2^{10}=58025$ yes

can you explain please

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We can user complement principle here!

Cases where A gets atleast one book = total cases - A doesn't get any book

Total cases: as each book is distinct each book can be given to A ,B or C. So 3 choices for each book. total 3^10.

Cases where A doesn't get any book : same as above but only B and C are two choices so 2^10.